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tringlcb.c
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C/C++ Source or Header
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1992-03-16
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11KB
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288 lines
#include <math.h>
#define SIGN3( A ) (((A).x<0)?4:0 | ((A).y<0)?2:0 | ((A).z<0)?1:0)
#define CROSS( A, B, C ) { \
(C).x = (A).y * (B).z - (A).z * (B).y; \
(C).y = -(A).x * (B).z + (A).z * (B).x; \
(C).z = (A).x * (B).y - (A).y * (B).x; \
}
#define SUB( A, B, C ) { \
(C).x = (A).x - (B).x; \
(C).y = (A).y - (B).y; \
(C).z = (A).z - (B).z; \
}
#define LERP( A, B, C) ((B)+(A)*((C)-(B)))
#define MIN3(a,b,c) ((((a)<(b))&&((a)<(c))) ? (a) : (((b)<(c)) ? (b) : (c)))
#define MAX3(a,b,c) ((((a)>(b))&&((a)>(c))) ? (a) : (((b)>(c)) ? (b) : (c)))
#define INSIDE 0
#define OUTSIDE 1
typedef struct {
float x;
float y;
float z;
} Point3;
typedef struct{
Point3 v1; /* Vertex1 */
Point3 v2; /* Vertex2 */
Point3 v3; /* Vertex3 */
} Triangle3;
/*___________________________________________________________________________*/
/* Which of the six face-plane(s) is point P outside of? */
long face_plane(Point3 p)
{
long outcode;
outcode = 0;
if (p.x > .5) outcode |= 0x01;
if (p.x < -.5) outcode |= 0x02;
if (p.y > .5) outcode |= 0x04;
if (p.y < -.5) outcode |= 0x08;
if (p.z > .5) outcode |= 0x10;
if (p.z < -.5) outcode |= 0x20;
return(outcode);
}
/*. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . */
/* Which of the twelve edge plane(s) is point P outside of? */
long bevel_2d(Point3 p)
{
long outcode;
outcode = 0;
if ( p.x + p.y > 1.0) outcode |= 0x001;
if ( p.x - p.y > 1.0) outcode |= 0x002;
if (-p.x + p.y > 1.0) outcode |= 0x004;
if (-p.x - p.y > 1.0) outcode |= 0x008;
if ( p.x + p.z > 1.0) outcode |= 0x010;
if ( p.x - p.z > 1.0) outcode |= 0x020;
if (-p.x + p.z > 1.0) outcode |= 0x040;
if (-p.x - p.z > 1.0) outcode |= 0x080;
if ( p.y + p.z > 1.0) outcode |= 0x100;
if ( p.y - p.z > 1.0) outcode |= 0x200;
if (-p.y + p.z > 1.0) outcode |= 0x400;
if (-p.y - p.z > 1.0) outcode |= 0x800;
return(outcode);
}
/*. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . */
/* Which of the eight corner plane(s) is point P outside of? */
long bevel_3d(Point3 p)
{
long outcode;
outcode = 0;
if (( p.x + p.y + p.z) > 1.5) outcode |= 0x01;
if (( p.x + p.y - p.z) > 1.5) outcode |= 0x02;
if (( p.x - p.y + p.z) > 1.5) outcode |= 0x04;
if (( p.x - p.y - p.z) > 1.5) outcode |= 0x08;
if ((-p.x + p.y + p.z) > 1.5) outcode |= 0x10;
if ((-p.x + p.y - p.z) > 1.5) outcode |= 0x20;
if ((-p.x - p.y + p.z) > 1.5) outcode |= 0x40;
if ((-p.x - p.y - p.z) > 1.5) outcode |= 0x80;
return(outcode);
}
/*. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . */
/* Test the point "alpha" of the way from P1 to P2 */
/* See if it is on a face of the cube */
/* Consider only faces in "mask" */
long check_point(Point3 p1, Point3 p2, float alpha, long mask)
{
Point3 plane_point;
plane_point.x = LERP(alpha, p1.x, p2.x);
plane_point.y = LERP(alpha, p1.y, p2.y);
plane_point.z = LERP(alpha, p1.z, p2.z);
return(face_plane(plane_point) & mask);
}
/*. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . */
/* Compute intersection of P1 --> P2 line segment with face planes */
/* Then test intersection point to see if it is on cube face */
/* Consider only face planes in "outcode_diff" */
/* Note: Zero bits in "outcode_diff" means face line is outside of */
long check_line(Point3 p1, Point3 p2, long outcode_diff)
{
if ((0x01 & outcode_diff) != 0)
if (check_point(p1,p2,( .5-p2.x)/(p1.x-p2.x),0x3e) == INSIDE) return(INSIDE);
if ((0x02 & outcode_diff) != 0)
if (check_point(p1,p2,(-.5-p2.x)/(p1.x-p2.x),0x3d) == INSIDE) return(INSIDE);
if ((0x04 & outcode_diff) != 0)
if (check_point(p1,p2,( .5-p2.y)/(p1.y-p2.y),0x3b) == INSIDE) return(INSIDE);
if ((0x08 & outcode_diff) != 0)
if (check_point(p1,p2,(-.5-p2.y)/(p1.y-p2.y),0x37) == INSIDE) return(INSIDE);
if ((0x10 & outcode_diff) != 0)
if (check_point(p1,p2,( .5-p2.z)/(p1.z-p2.z),0x2f) == INSIDE) return(INSIDE);
if ((0x20 & outcode_diff) != 0)
if (check_point(p1,p2,(-.5-p2.z)/(p1.z-p2.z),0x1f) == INSIDE) return(INSIDE);
return(OUTSIDE);
}
/*. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . */
/* Test if 3D point is inside 3D triangle */
long point_triangle_intersection(Point3 p, Triangle3 t)
{
long sign12,sign23,sign31;
Point3 vect12,vect23,vect31,vect1h,vect2h,vect3h;
Point3 cross12_1p,cross23_2p,cross31_3p;
/* First, a quick bounding-box test: */
/* If P is outside triangle bbox, there cannot be an intersection. */
if (p.x > MAX3(t.v1.x, t.v2.x, t.v3.x)) return(OUTSIDE);
if (p.y > MAX3(t.v1.y, t.v2.y, t.v3.y)) return(OUTSIDE);
if (p.z > MAX3(t.v1.z, t.v2.z, t.v3.z)) return(OUTSIDE);
if (p.x < MIN3(t.v1.x, t.v2.x, t.v3.x)) return(OUTSIDE);
if (p.y < MIN3(t.v1.y, t.v2.y, t.v3.y)) return(OUTSIDE);
if (p.z < MIN3(t.v1.z, t.v2.z, t.v3.z)) return(OUTSIDE);
/* For each triangle side, make a vector out of it by subtracting vertexes; */
/* make another vector from one vertex to point P. */
/* The crossproduct of these two vectors is orthogonal to both and the */
/* signs of its X,Y,Z components indicate whether P was to the inside or */
/* to the outside of this triangle side. */
SUB(t.v1, t.v2, vect12)
SUB(t.v1, p, vect1h);
CROSS(vect12, vect1h, cross12_1p)
sign12 = SIGN3(cross12_1p); /* Extract X,Y,Z signs as 0...7 integer */
SUB(t.v2, t.v3, vect23)
SUB(t.v2, p, vect2h);
CROSS(vect23, vect2h, cross23_2p)
sign23 = SIGN3(cross23_2p);
SUB(t.v3, t.v1, vect31)
SUB(t.v3, p, vect3h);
CROSS(vect31, vect3h, cross31_3p)
sign31 = SIGN3(cross31_3p);
/* If all three crossproduct vectors agree in their component signs, */
/* then the point must be inside all three. */
/* P cannot be OUTSIDE all three sides simultaneously. */
if ((sign12 == sign23) && (sign23 == sign31))
return(INSIDE);
else
return(OUTSIDE);
}
/*. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . */
/**********************************************/
/* This is the main algorithm procedure. */
/* Triangle t is compared with a unit cube, */
/* centered on the origin. */
/* It returns INSIDE (0) or OUTSIDE(1) if t */
/* intersects or does not intersect the cube. */
/**********************************************/
long t_c_intersection(Triangle3 t)
{
long v1_test,v2_test,v3_test;
float d;
Point3 vect12,vect13,vect23,vect31,norm;
Point3 hitpp,hitpn,hitnp,hitnn;
/* First compare all three vertexes with all six face-planes */
/* If any vertex is inside the cube, return immediately! */
if ((v1_test = face_plane(t.v1)) == INSIDE) return(INSIDE);
if ((v2_test = face_plane(t.v2)) == INSIDE) return(INSIDE);
if ((v3_test = face_plane(t.v3)) == INSIDE) return(INSIDE);
/* If all three vertexes were outside of one or more face-planes, */
/* return immediately with a trivial rejection! */
if ((v1_test & v2_test & v3_test) != 0) return(OUTSIDE);
/* Now do the same trivial rejection test for the 12 edge planes */
v1_test |= bevel_2d(t.v1) << 8;
v2_test |= bevel_2d(t.v2) << 8;
v3_test |= bevel_2d(t.v3) << 8;
if ((v1_test & v2_test & v3_test) != 0) return(OUTSIDE);
/* Now do the same trivial rejection test for the 8 corner planes */
v1_test |= bevel_3d(t.v1) << 24;
v2_test |= bevel_3d(t.v2) << 24;
v3_test |= bevel_3d(t.v3) << 24;
if ((v1_test & v2_test & v3_test) != 0) return(OUTSIDE);
/* If vertex 1 and 2, as a pair, cannot be trivially rejected */
/* by the above tests, then see if the v1-->v2 triangle edge */
/* intersects the cube. Do the same for v1-->v3 and v2-->v3. */
/* Pass to the intersection algorithm the "OR" of the outcode */
/* bits, so that only those cube faces which are spanned by */
/* each triangle edge need be tested. */
if ((v1_test & v2_test) == 0)
if (check_line(t.v1,t.v2,v1_test|v2_test) == INSIDE) return(INSIDE);
if ((v1_test & v3_test) == 0)
if (check_line(t.v1,t.v3,v1_test|v3_test) == INSIDE) return(INSIDE);
if ((v2_test & v3_test) == 0)
if (check_line(t.v2,t.v3,v2_test|v3_test) == INSIDE) return(INSIDE);
/* By now, we know that the triangle is not off to any side, */
/* and that its sides do not penetrate the cube. We must now */
/* test for the cube intersecting the interior of the triangle. */
/* We do this by looking for intersections between the cube */
/* diagonals and the triangle...first finding the intersection */
/* of the four diagonals with the plane of the triangle, and */
/* then if that intersection is inside the cube, pursuing */
/* whether the intersection point is inside the triangle itself. */
/* To find plane of the triangle, first perform crossproduct on */
/* two triangle side vectors to compute the normal vector. */
SUB(t.v1,t.v2,vect12);
SUB(t.v1,t.v3,vect13);
CROSS(vect12,vect13,norm)
/* The normal vector "norm" X,Y,Z components are the coefficients */
/* of the triangles AX + BY + CZ + D = 0 plane equation. If we */
/* solve the plane equation for X=Y=Z (a diagonal), we get */
/* -D/(A+B+C) as a metric of the distance from cube center to the */
/* diagonal/plane intersection. If this is between -0.5 and 0.5, */
/* the intersection is inside the cube. If so, we continue by */
/* doing a point/triangle intersection. */
/* Do this for all four diagonals. */
d = norm.x * t.v1.x + norm.y * t.v1.y + norm.z * t.v1.z;
hitpp.x = hitpp.y = hitpp.z = d / (norm.x + norm.y + norm.z);
if (fabsf(hitpp.x) <= 0.5)
if (point_triangle_intersection(hitpp,t) == INSIDE) return(INSIDE);
hitpn.z = -(hitpn.x = hitpn.y = d / (norm.x + norm.y - norm.z));
if (fabsf(hitpn.x) <= 0.5)
if (point_triangle_intersection(hitpn,t) == INSIDE) return(INSIDE);
hitnp.y = -(hitnp.x = hitnp.z = d / (norm.x - norm.y + norm.z));
if (fabsf(hitnp.x) <= 0.5)
if (point_triangle_intersection(hitnp,t) == INSIDE) return(INSIDE);
hitnn.y = hitnn.z = -(hitnn.x = d / (norm.x - norm.y - norm.z));
if (fabsf(hitnn.x) <= 0.5)
if (point_triangle_intersection(hitnn,t) == INSIDE) return(INSIDE);
/* No edge touched the cube; no cube diagonal touched the triangle. */
/* We're done...there was no intersection. */
return(OUTSIDE);
}